How to Construct the Perpendicular Bisector of a Line Segment
Table of Contents
- Logic behind Drawing a Perpendicular Bisector of a Line Segment
- What’s Next?
In the previous segment, we learnt how to draw a perpendicular bisector of a line segment. Here, let us learn about the logic behind it.
Construction of perpendicular bisector:
The construction of a perpendicular bisector of a line segment is as shown below:
Let’s understand how the constructed line (line CD) is a perpendicular bisector of the given line
segment (seg AB). That is, to prove line CD ⟂ seg AB and seg AP ≅ seg BP.
Join CA, CB, DA, and DB.
Construction for proof
| No
. |
Statement | Reason |
| 1 | CA = CB = DA = DB | The compass width used to draw the arcs was the same. |
| Consider ?CAB and ?DAB. | ||
| 2 | seg CA ≅ seg DA | From statement 1 |
| 3 | seg CB ≅ seg DB | From statement 1 |
| 4 | seg AB ≅ seg AB | Common side |
| 5 | ∴ ?CAB ≅ ?DAB | By SSS test of congruency. |
| 6 | ∴ ∠CAB ≅ ∠DAB | Corresponding angles of congruent triangles are congruent. |
| 7 | ∴ ∠CBA ≅ ∠DBA | Corresponding angles of congruent triangles are congruent. |
| Consider ?CAB | ||
| 8 | seg CA ≅ seg CB | From statement 1. |
| 9 | ∴ ∠CAB ≅ ∠CBA | Opposite angles of congruent sides are congruent in a triangle. |
| Consider ?DAB | ||
| 10 | seg DA ≅ seg DB | From statement 1 |
| 11 | ∴ ∠DAB ≅ ∠DBA | Opposite angles of congruent sides |
